Muse,
There isn't any controlled data on people doing fasting while young because you can't impose things like that just for the sake of experiments. Imagine setting up two groups of teenagers normalized for everything else (already hard enough), then you make one group eat less, and find that they are all a bit less developed/shorter/etc than the other group, then all you can do is sit down and wait for the lawsuits.
For people doing it for religious reasons while teenagers as you mentioned what's missing is the corresponding control (a group equal in all other relevant respects except fasting during adolescence) to draw conclusions, basically those people might have gotten a little taller or more developed if they didn't fast during puberty but you don't have a baseline to compare. And with statistical studies after the fact you can't really separate coincidences based on other factors (genetics, other cultural activities, etc) from actual effects of fasting (plus the way people do it can vary a lot which makes it harder to draw conclusions). Still, even from those social-science-like studies you can see the impact of better nutrition in the on-average higher stature of kids compared to their parents.
You can do those more controlled tests with animal studies however, and that's one of the reasons we know that nutrition is critical at those stages, and if your body is already decided on growing it will take advantage of any extra nutrition and translate that into additional growth.
As far as the biochemistry of it, all those good hormones are again stimulated by the amount of nutrients available, and if you don't have enough good fat around for example your body will just stop making them and stunt you in many ways (look for example at the effects of eating disorders on teenage girls menstrual cycle, although that's obviously a more extreme case).
Anyways, I concur with Chris we are not giving conflicting opinions, because as they say the devil is in the details, we are simply pointing out potential advantages in normal situations (e.g., well-controlled fasting that is done for good reasons and with a plan) and risks in more specific situations (depriving yourself of potentially healthy nutrients when it's not even called for and where it -could- have long-term, irreparable effects), and then saying whether we think it's worth it in a specific situation.
In the case of growing periods we are just being a lot more cautious because, well, you don't get two shots at puberty, you mess it up and you don't get a chance to do it over. So then while I might normally say "you're not going to die or anything from just skipping meals", in this situation I would ask "can you be sure that this is not going to impair your growth in some way, especially when you are not doing frequent tests to make sure you are not going overboard in any one direction?" And more importantly, is it worth it taking that potential risk in your case?
Which brings me to my view of the specifics:
Spencer,
In your case I think you are looking at this as a quick patch which is not even really needed rather than focusing first on things that are more important. First off you mentioned you don't have much control on your nutrition and that's why you are considering this. I think you should focus on getting a bit more control of that and eating as healthy as you can first instead. Second, as Chris said, you shouldn't worry about trying to control your hormones. Chances are, even if you had ways to control them you are more likely to mess things up in major ways.
And third, 12% bodyfat is not a bad thing for your situation, you should focus on other goals and let your already low teenager bodyfat% fluctuate accordingly to help you grow well and remain healthy.
If you are eating well, training well and developing well it will go to its ideal level on its own.
-And-, if you are using things like emotions and body image rather than planning, knowledge and logic to choose your diet, you are going down a much more dangerous path, because those things tend to get more and more distorted rather than remaining impartial and based on solid results and physiology.
